Technical Field
Embodiments of the subject matter disclosed herein generally relate to seismic data analysis or, more specifically, to using statistical moments of seismic data to extract anisotropic information such as fracture and stress properties.
Discussion of the Background
In the field of oil and gas exploration and recovery, analysis of seismic data obtained through seismic surveys provides valuable information about structure and physical parameters of subterranean rock formations. In a seismic survey, a source generates a seismic signal that propagates into the explored formation and is, at least partially, reflected at interfaces between a formation's layer having different acoustic impedances. The seismic signal is typically a compressional pressure variation along the propagation direction (P-wave), but both P-waves and S-waves (i.e., shear waves) may be detected. Seismic detectors record seismic data which represent the detected waves. In fact, the recorded seismic data includes a convolution of the source wavelet (i.e., the signal's signature) and the formation's response function. Seismic data processing extracts the formation's response function, and then various parameters related to the explored formation. One way of expressing the response function is reflectivity, R, which for detected P-waves is Rpp. Reflectivity may be expressed as a function of the incidence angle, θ, (which is defined in a vertical plane relative to the source position) and of the azimuth angle, ϕ (which is defined in a horizontal plane around the source position). From the point of view of this approach, seismic data and reflectivity are the same.
Seismic data processing methods include azimuthal velocity correction, amplitude versus offset (AVO) analysis and inversion, amplitude versus offset and azimuth analysis (AVOAz) and inversion of conventional three-dimensional (3D) seismic data, and birefringence analysis of multicomponent 3D seismic data. Reflectivity characterizes subterranean properties and can serve as input to other inversion algorithms. For example, reflectivity can provide useful information regarding the anisotropy parameters of the subterranean formation, such as subsurface fractures. These anisotropy parameters may reveal shale plays, tight gas sands and coal bed methane, as well as carbonates in naturally fractured reservoirs. Note that these remarks are true also for seismic data in general. These characteristics and parameters are used to design and manage underground transportation systems, foundations of major structures, cavities for storage of liquids, gases or solids, etc. In oil and gas exploration, this kind of information is used for determining optimal locations and orientations of wells (which may be vertical, inclined or deviated, and horizontal), to minimize wellbore instability and formation break-out. This information may also be used for stimulating the production of hydrocarbons by applying hydraulic pressure on the formation from the wellbore. The data inversions yield estimates of the elastic stiffnesses (velocities and anisotropic parameters) that can be used to predict lithology, porosity and the fluid content of the subsurface, as well as intensity and orientation of fractures in subterranean formations.
Conventional AVO inversions provide only band-limited fractional elastic parameters estimates with reduced resolution and quality (i.e., the bandwidth of seismic data is always less than the bandwidth of the desired reflectivities). Conventional AVOAz inversions are typically based on the near offset approximation of the equation set forth by Rügger, A., 2002, “Reflection coefficients and azimuthal AVO Analysis in anisotropic media,” SEG geophysical monograph series number 10: Soc. Expl. Geophys (hereinafter “Rüger”). Rüger provides the equation showing the amplitude R with azimuth φ for narrow angles of incidence θ. However, this method has a number of limitations. For example, the near offset Rüger equation is not theoretically valid for the case of two anisotropic half-spaces with different anisotropy orientation. Further, there is a 90-degree ambiguity associated with the estimate of the isotropy plane.
Recently, separating azimuthal AVO into AVO (Amplitude Versus Offset) and AVAz (Amplitude Versus Azimuth) has been achieved using Fourier coefficients (FCs) as described in U.S. Pat. No. 8,792,303 (the content of which is incorporated in its entirety herein by reference). This separation advantageously avoids coupling between the isotropic and anisotropic properties.
Accordingly, it is desirable to enhance existing methods and provide new methods to extract anisotropic properties without the drawbacks and limitations of conventional methods.